STATIC FLUID CYLINDERS AND PLANE LAYERS IN GENERAL RELATIVITY

Static perfect fluid distributions in general relativity which possess cylindrical, toroidal or pseudoplanar symmetry (these symmetries are locally equivalent) are considered. Solutions in quadratures are obtained for fluids with an unspecified equation of state and for rho c2=np, where n is a constant, with or without an electromagnetic field Fmu nu compatible with the symmetry assumed. Moreover, for rho c2=np, F mu nu identical to 0, solutions are given in an explicit closed form. Some physical properties of the solutions are discussed.